Craze stresses

Processes that occur at a size scale larger than the individual chain have been studied using microscopy, mainly transmission electron microscopy (TEM), but optical microscopy has been useful to examine craze shapes. The knowledge of the crazing process obtained by TEM has been ably summarised by Kramer and will not be repeated here [2,3]. At an interface between two polymers a craze often forms within one of the materials, typically the one with lower crazing stress. 

Overall behavior. It is the time-dependent strain at which crazing, stress whitening, and rupture decreases with a... 

It is interesting to remark that like most mechanical parameters the crazing stress exhibits viscoelastic characteristics, decreasing with increasing temperature and with decreasing strain rate (which is an indication that it is better to speak of a crazing strain). We come back to the discussion of crazes in Sect. 13.5.5. 

More work on a detailed description of the fibrillation process is needed to clarify the underlying mechanism and its relationship with molecular aspects, such as the entanglement density or the molecular mobility. Nevertheless, based on the observations reported by DOll [29,30] of time-dependent craze stress and Kramer s [31,32] description of fibrillation involving an active plastic zone, one can conclude that craze thickening is a viscoplastic process. 

Craze breakdown is experimentally characterized by a critical craze thickness Acr which is primarily dependent (Eq. 20) on the craze stress ac, the force for chain scission, and the entangled chain density along the craze surface vs. The craze stress ac is assumed to be rate and temperature depen-... 

The cohesive surface description presented here has some similarities to the thermal decohesion model of Leevers [56], which is based on a modified strip model to account for thermal effects, but a constant craze stress is assumed. Leevers focuses on dynamic fracture. The thermal decohesion model assumes that heat generated during the widening of the strip diffuses into the surrounding bulk and that decohesion happens when the melt temperature is reached over a critical length. This critical length is identified as the molecular chain contour. 

It follows that for a constant refractive index the craze strain is also constant. Our observations on polystyrene indicate that neither the craze refractive index nor the ratios kB/kc and kB/kh are constant along the length of the craze (Figure 6). The values of A calculated from Equation 4 are shown in Figure 7. That the craze strain is not constant does not preclude the possibility that the craze stress is still constant, as might be the case for an ideal plastic material. However, the experiments on craze stress-strain properties by Kambour (10) and Hoare and Hull (11) indicate that this is not the case. 

The dislocation method of stress analysis is also useful for determining craze stress fields in anisotropic (e.g., oriented) polymers . All one needs here is the stress field of a single dislocation in a single crystal with the same symmetry as the oriented polymer (the text by Hirth and Lothe provides a number of simple cases plus copious references to more complete treatments in the literature) the craze stress field can be generated by superposition of the stress fields of an array of these dislocations of density a(x). Dislocations may also be used to represent the self-stress fields of curvilinear crazes (produced by craze growth in a non-homogeneous stress field for example). Such a method has been developed by Mills... 

Craze fibril diameters determined by TEM and SAXS are of the order of 10 nm. Craze fibril volume fractions Vf range from 0.5 to 0.1, depending on the entanglement network of the polymer and the local craze stress. 

Using a modified Dugdale model with a variable craze stress along the craze zone this effect has quahtatively been interpreted At positions where the constant stress Dugdale model gives displacements higher than the measured ones the actual craze stress must be higher. In the case of PC a closer inspection reveals a stress peak at the crack and craze tip. Kambour predicted just such a stress distribution in a craze from the analysis of the stress distribution around a craze (without a crack)... 

Fig. 12 a and b. Material data of the micro region at the crack tip as derived by the application of the Dugdale model to measured craze sizes (Fig. 11) a craze stress 0 b creep modulus E... 

From the reported craze dimensions, the tensile creep moduli E and craze stress have been derived by the aid of the Dugdale model. For PMMA the thus evaluated creep moduli are shown as a function of temperature T in Fig. 18 together... 

In Fig. 19 the derived craze stresses a, are shown as a function of temperature T for various polymers For the PMMA results reported by Schirrer, Goett >... 

For temperatures below 10 °C the results of Morgan and Ward on PMMA suggest a constant craze stress. However, this may reflect their use of the Young s modulus in their evaluation, which shows a steeper variation with temperature than... 

Fig. 19. Craze stress cr as a function of temperature T in different polymers PMMA (x...

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